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Robustness of solutions to the capacitated facility location problem with uncertain demand

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Abstract

We investigate the properties of robust solutions of the Capacitated Facility Location Problem with uncertain demand. We show that the monotonic behavior of the price of robustness is not guaranteed, and therefore that one cannot discriminate among alternative robust solutions by simply relying on the trade-off price-vs-robustness. Furthermore, we report a computational study on benchmark instances from the literature and on instances derived from a real-world application, which demonstrates the validity in practice of our findings.

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Notes

  1. More precisely, we have that \( \frac{\sum _{i=1}^{n_s} FV((\mathbf {y}^*,\mathbf {x}^*),\mathbf{d} _i)}{n_s} \rightarrow {\mathbb {E}}_\mathbf{d \in U({\hat{\varepsilon }})} (FV((\mathbf {y}^*,\mathbf {x}^*),\mathbf{d} ))\) for \(n_s \rightarrow \infty \).

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Authors and Affiliations

  1. Department of Electrical, Electronic, and Information Engineering “Guglielmo Marconi”, University of Bologna, Via Venezia 52, 47521, Cesena, Italy

    Roberto Baldacci

  2. IE University, Maria de Molina 31B, 28006, Madrid, Spain

    Marco Caserta

  3. Université Sorbonne Paris Nord, LIPN, CNRS, UMR7030, F-93430, Villetaneuse, France

    Emiliano Traversi & Roberto Wolfler Calvo

  4. DIM, Universitá di Cagliari, Cagliari, France

    Roberto Wolfler Calvo

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  1. Roberto Baldacci
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  2. Marco Caserta
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  3. Emiliano Traversi
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  4. Roberto Wolfler Calvo
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Correspondence to Roberto Wolfler Calvo.

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Baldacci, R., Caserta, M., Traversi, E. et al. Robustness of solutions to the capacitated facility location problem with uncertain demand. Optim Lett 16, 2711–2727 (2022). https://doi.org/10.1007/s11590-021-01848-4

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  • DOI: https://doi.org/10.1007/s11590-021-01848-4

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